intros 3 (y Uby E); cases (M ? E) (n En); unfold in Uby; cases (Uby ? En);
qed.
+include "ordered_group.ma".
+include "nat/orders.ma".
+definition tends ≝
+ λO:ogroup.λs:sequence O.
+ ∀e:O.0 < e → ∃N.∀n.N < n → -e < s n ∧ s n < e.
definition increasing ≝
λO:pordered_set.λa:sequence O.∀n:nat.a n ≤ a (S n).